Question

Question 4 (xiii)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(xiii) $\sqrt{3},\sqrt{6},\sqrt{9},\sqrt{12},\dots$

Answer 1

If the difference between any two consecutive terms of a series is a constant value, then the series is an A.P.

Given, the series is :
$\sqrt{3},\sqrt{6},\sqrt{9},\sqrt{12},\dots$
Here,
$a_2-a_1=\sqrt{6}-\sqrt{3}=\sqrt{3}\times 2-\sqrt{3}=\sqrt{3}(\sqrt{2}-1)a_3-a_2=\sqrt{9}-\sqrt{6}=3-\sqrt{6}=\sqrt{3}(\sqrt{3}-\sqrt{2})a_4-a_3=\sqrt{12}-\sqrt{9}=2\sqrt{3}-\sqrt{3\times 3}=\sqrt{3}(2-\sqrt{3})$

Note that the difference between any two consecutive terms of the series is not a constant value.
Hence, the given series is not an AP.